Vancouver Island University
Spring 2010
Math 310
Introduction to Graph Theory
Instructor: Dr. Valerie Watts
Office: Building 360, Room 303C
Phone: 740-6147, Local 6147
Email: Valerie.Watts@viu.ca
URL: http://web.viu.ca/wattsv
Office Hours: Monday 11:30 am-1:00 pm
Tuesday 9:30 am-11:00 am
Wednesday 11:30 am-12:30 pm
Or by appointment
Class Schedule
Day
Tuesday
Friday
Time
11:30 am-1:00 pm
11:30 am-1:00 pm
Location
Building 360, Room 323
Building 360, Room 323
Prerequisite
Minimum of "C" in either MATH 223 or both of MATH 123 and MATH 241.
Course Objective and Content
The objective of this course is to introduce students to the combinatorial, algorithmic and algebraic
aspects of graph theory. The course will cover the following topics:
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Graphs and Subgraphs: graphs, isomorphisms, incidence and adjacency matrices, subgraphs,
vertex degrees, connected graphs
Trees: trees, spanning trees, cut edges, cut vertices
Connectivity: vertex and edge connectivity, blocks, Menger’s Theorem
Euler Tours and Hamilton Cycles
Matchings: matchings, matchings and coverings in bipartite graphs, perfect matchings,
factorizations
Edge Colourings: edge chromatic number, Vizing’s Theorem
Independent Sets and Cliques
Vertex Colourings: chromatic number, Brook’s Theorem
Planar Graphs: plane and planar graphs, dual graphs, Euler’s formula, Kuratowski’s Theorem,
the Four Colour Theorem
Ramsey Theory: Ramsey numbers, Turan’s Theorem (time permitting)
Text
The required text for the course is Graph Theory with Applications by Bondy and Murty. You can find
the 1976 edition online at http://www.ecp6.jussieu.fr/pageperso/bondy/books/gtwa/gtwa.html. This
version will be sufficient for our needs in this course and is the version I will refer to during the class.
The authors recently published a new (and improved) edition, entitled Graph Theory (ISBN:
1846289696), which you can buy if you want an actual book.
Class Website
The class website can be found at http://web.viu.ca/wattsv/math310.htm. The website will include
information about tests, weekly assignments and solutions to the tests and assignments.
Assignments
The best way to learn math is to DO math and so homework is an essential component of the course. I
will collect a homework assignment every Wednesday, except the weeks of the tests. The weekly
homework assignments will be posted on my website (under Assignments). I may also include additional
practice problems on each assignment. You should attempt all of the problems that I assign, even if they
are not collected for grading. I will post solutions to each assignment on the website.
I expect homework to be completed according to the guidelines stated below:
 Homework is to be handed in to me by 12:30 pm on the day it is due, no exceptions.
 I will use the grading rubric below to evaluate each problem:
5-the correct answer with the details spelled out
4-correct answer with some minor errors
3 and 2-various levels of somewhat valid by mistaken attempts
1-tried, but not even close
0-didn’t even try the problem
 Late assignments will be accepted with a 10% per day penalty (up to a maximum of two days).
 Your name should be written on your homework. Multiple pages must be stapled together. You
may write on both sides of the paper.
 Each problem must be neatly and legibly written, with all intermediate steps included and
showing calculations and reasoning in a clear, logical manner. A problem not written in this way
may not be graded and given a score of 0.
 Correct answers which are not accompanied by coherent back-up work will be given 0.
 Homework should reflect your understanding of the material. Homework will not be graded on
effort, but on understanding and correctness. Keep in mind that solutions will be worth more
than answers.
You are strongly encouraged to discuss homework problems with me and with each other. However, you
MUST write up your own solutions; copying is absolutely forbidden. Any student found copying or
allowing others to copy their work will receive a 0 for that particular assignment and may face additional
penalties administered by the school. You should be familiar with the school’s regulations regarding
academic integrity and code of conduct.
One final note: do not leave homework until the last minute!
Tests and Final Exam
All in-class tests will be closed book and individual work. There will be two in-class tests. The in-class
test dates are February 9, 2010 and March 30, 2010. In addition, I will include a take-home portion
with each test. I will give out more details about the take-home portion later.
The final exam will be comprehensive and will be held during the final exam period April 14-23, 2010. I
may also include a take-home portion with the final exam. Remember, do not make any travel plans until
the final exam schedule is known.
Any questions regarding the grading of tests need to be cleared up within one week after the test has been
graded and returned to you.
You are expected to be present for all tests/exams. Make-up tests will not be given. If you miss a test
due to a verifiable emergency, you must notify me as soon as possible and provide me with
documentation as to why you missed the test. In this circumstance, I will transfer the percentage of the
missed test to your final exam. This concession is only for students who miss a test due to extreme
circumstances and is available only at my discretion. Students who miss a test for any other reason or
who cannot provide adequate documentation of a real emergency will be given a grade of zero.
Any student found copying or allowing others to copy their test/exam will receive a zero for that test.
Evaluation
Assignments: 20% (I will drop you lowest assignment score)
In-Class Tests: 20% each (there are two tests)
Final Exam: 40%
Final letter grades will be assigned on your overall course percentage:
A+ 95-100%
B+ 80-84%
C+ 65-69%
D 50-54%
A 90-95%
B 75-79%
C 60-64%
F 0-49%
A- 85-89%
B- 70-74%
C- 55-59%
If you have questions or concerns regarding graded material, I am happy to discuss it with you.
However, you must meet with me no later than ONE WEEK after the graded item has been returned in
order to have a chance at receiving points back.
Electronic Devices
All cell phones, blackberries, pagers, etc. must be turned off during class. Also, no student will be
allowed to wear headphones to listen to music during class time.